Slides electrical instrumentation lecture 2
-
Upload
tu-delft-opencourseware -
Category
Documents
-
view
703 -
download
4
Transcript of Slides electrical instrumentation lecture 2
![Page 1: Slides electrical instrumentation lecture 2](https://reader031.fdocuments.in/reader031/viewer/2022020105/556491c7d8b42a5f6c8b4e93/html5/thumbnails/1.jpg)
1
ET8.017El. Instr.Delft University of Technology
Electronic Instrumentation
Lecturer: Kofi Makinwa
015-27 86466Room. HB13.270 EWI building
Also involved:Saleh Heidary([email protected])
ET8.017El. Instr.Delft University of Technology
Monday Sept. 16: Transduction of information (Chapter 2) - Sensitivity and cross-sensitivities- Resistive transducers- Capacitive transducers
Content and Schedule
Wednesday Sept. 18: Submit Assignment 1Detection limit due to offset
![Page 2: Slides electrical instrumentation lecture 2](https://reader031.fdocuments.in/reader031/viewer/2022020105/556491c7d8b42a5f6c8b4e93/html5/thumbnails/2.jpg)
2
ET8.017El. Instr.Delft University of Technology
What Is A Sensor?
A device that converts information from one energy domain into the electrical domainWhere it can be easily (digitally) processed and stored
ET8.017El. Instr.Delft University of Technology
010010111010001011110000111101101101011010011110000111111010101010101000001101111111111111010101010000000000010101000110111010101010111101010011110110101010011010101110011110100001010100110010011101011001010101101101000111010101101110111101010101011101101110110110111101000001111011000000001111010101100110111111111111101010010000111100010101010100111111111110101001001001010101000000000011010101010101000010110101010111010101001001011101000101111000011110110110101101001111000011111101010101010100000110111111111111101010101000000000001010100011011101010101011110101001111011010101001101010111001111010000101010011001001110101100101010110110100011101010110111011110101010101110110111011011011110100000111101100000000111101010110011011111111111110101001000011110001010101010011111111111010100100100101010100000000001101010101010100001011010101011101010100100101110100010111100001111011011010110100111100001111110101010101010000011011111111111110101010100000000000101010001101110101010101111010100111101101010100110101011100111101000010101001100100111010110010101011011010001110101011011101111010101010111011011101101101111010000011110110000000011110101011001101111111111111010100100001111000101010101001111111111101010010010010101010000000000110101010101010000101101010101110101010101111001011111110100000101010000001110110110001101001010101111
The World Is Analog
So sensors output analog informationRequires analog-to-digital conversionNote: transducer = sensor OR actuator
![Page 3: Slides electrical instrumentation lecture 2](https://reader031.fdocuments.in/reader031/viewer/2022020105/556491c7d8b42a5f6c8b4e93/html5/thumbnails/3.jpg)
3
ET8.017El. Instr.Delft University of Technology
• Source loading by the measurement• Sensitivity to unintended el. and non-el. quantities• Electro-magnetic interference• Thermal noise• Many more…..
Signal domains:
Sources of uncertainty (error) :
• Magnetic (Ma), • Mechanical (Me),• Thermal (Th),• Optical (Op),• Chemical (Ch) and• Electrical (El).
Transduction
ET8.017El. Instr.Delft University of Technology
Transduction matrix:
Transduction
ma,ma me,ma th,ma opt,ma ch,ma el,ma
ma,me me,me th,me opt,me ch,me el,me
ma,th me,th th,th opt,th ch,th el,th
ma,opt me,opt th,opt opt,opt ch,opt el,opt
ma,ch me,ch
Ma t t t t t tMe t t t t t tTh t t t t t t = Opt t t t t t tCh tEl
⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠
os
os
os
os
th,ch opt,ch ch,ch el,ch os
ma,el me,el th,el opt,el ch,el el,el os
Ma MaMe MeTh Th +Opt OptCht t t t t ChElt t t t t t El
⎛ ⎞ ⎛ ⎞⎛ ⎞⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟
⎝ ⎠ ⎝ ⎠⎝ ⎠
![Page 4: Slides electrical instrumentation lecture 2](https://reader031.fdocuments.in/reader031/viewer/2022020105/556491c7d8b42a5f6c8b4e93/html5/thumbnails/4.jpg)
4
ET8.017El. Instr.Delft University of Technology
Transduction matrix:
Transduction
ma,ma me,ma th,ma opt,ma ch,ma el,ma
ma,me me,me th,me opt,me ch,me el,me
ma,th me,th th,th opt,th ch,th el,th
ma,opt me,opt th,opt opt,opt ch,opt el,opt
ma,ch me,ch
Ma t t t t t tMe t t t t t tTh t t t t t t = Opt t t t t t tCh tEl
⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠
os
os
os
os
th,ch opt,ch ch,ch el,ch os
ma,el me,el th,el opt,el ch,el el,el os
Ma MaMe MeTh Th +Opt OptCht t t t t ChElt t t t t t El
⎛ ⎞ ⎛ ⎞⎛ ⎞⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟
⎝ ⎠ ⎝ ⎠⎝ ⎠
Acceleration to displ. = Transduction from mechanical to mechanical
ET8.017El. Instr.Delft University of Technology
Transduction matrix (red text ⇒ non-zero coefs):
Transduction
ma,ma me,ma th,ma opt,ma ch,ma el,ma
ma,me th,me opt,me ch,me el,me
ma,th me,th th,th opt,th ch,th el,th
ma,opt me,opt th,opt opt,opt ch,opt el,opt
ma,ch me,c
me,me
h
Ma t t t t t tt t t t t
Th t t t t t t = Opt t t t t t tCh tE
Me
l
t⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠
os
os
os
th,ch opt,ch ch,ch el,ch os
ma,el me,el th,el opt,el ch,el el,el o
os
s
Ma Ma
Th Th +Opt OptCht t t t t ChElt t t t t
Me
El
M
t
e⎛ ⎞ ⎛ ⎞⎛ ⎞⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟
⎝ ⎠ ⎝ ⎠⎝ ⎠
Acceleration to displ. = Transduction from mechanical to mechanical
![Page 5: Slides electrical instrumentation lecture 2](https://reader031.fdocuments.in/reader031/viewer/2022020105/556491c7d8b42a5f6c8b4e93/html5/thumbnails/5.jpg)
5
ET8.017El. Instr.Delft University of Technology
Transduction matrix:
Transduction
ma,ma me,ma th,ma opt,ma ch,ma el,ma
ma,me me,me th,me opt,me ch,me el,me
ma,th me,th th,th opt,th ch,th el,th
ma,opt me,opt th,opt opt,opt ch,opt el,opt
ma,ch me,ch
Ma t t t t t tMe t t t t t tTh t t t t t t = Opt t t t t t tCh tEl
⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠
os
os
os
os
th,ch opt,ch ch,ch el,ch os
ma,el me,el th,el opt,el ch,el el,el os
Ma MaMe MeTh Th +Opt OptCht t t t t ChElt t t t t t El
⎛ ⎞ ⎛ ⎞⎛ ⎞⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟
⎝ ⎠ ⎝ ⎠⎝ ⎠
ET8.017El. Instr.Delft University of Technology
Transduction matrix:
Transduction
ma,ma me,ma th,ma opt,ma ch,ma el,ma
ma,me me,me th,me opt,me ch,me el,me
ma,th me,th th,th opt,th ch,th el,th
ma,opt me,opt th,opt opt,opt ch,opt el,opt
ma,ch me,ch
Ma t t t t t tMe t t t t t tTh t t t t t t = Opt t t t t t tCh tEl
⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠
os
os
os
os
th,ch opt,ch ch,ch el,ch os
ma,el me,el th,el opt,el ch,el el,el os
Ma MaMe MeTh Th +Opt OptCht t t t t ChElt t t t t t El
⎛ ⎞ ⎛ ⎞⎛ ⎞⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟
⎝ ⎠ ⎝ ⎠⎝ ⎠
Transduction in two steps:1. from optical to thermal, followed by 2. thermal to mechanical
= tandem transducer
![Page 6: Slides electrical instrumentation lecture 2](https://reader031.fdocuments.in/reader031/viewer/2022020105/556491c7d8b42a5f6c8b4e93/html5/thumbnails/6.jpg)
6
ET8.017El. Instr.Delft University of Technology
Tandem transduction:
Transduction
Transduction in two steps:1. from optical to thermal, followed by 2. thermal to mechanical
= tandem transducer
( )ma,me me,me opt,me ch,me el,me
ma,ma me,ma th,ma opt,ma ch,ma el,ma
ma,me me,me th,me opt,me ch,me el,me
ma,th me,th th,th ch,th el,
t
topt,th h
ma,opt me,opt th,opt opt,opt ch,opt
h,
e
m
l,o
e
p
= s s s s s
t t t t t tt t t t t tt t t t t
t t t t t
Me
t
s •
os
os
os
t
ma,ch me,ch th,ch opt,ch ch,ch el,ch os
ma,el me,el th,el opt,el ch,el el,el
o
o
oss2
s1
Ma MaMe MeT
Opth Th + +
tCht t t t t t ChElt t t t t
t
l
p
t E
O Me
⎛ ⎞⎛ ⎞ ⎛ ⎞⎛ ⎞⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠ ⎝ ⎠⎝ ⎠⎝ ⎠
ET8.017El. Instr.Delft University of Technology
Tandem transduction requires an intermediate non-electrical domain:
Transduction
So:
1. Acceleration to displacement(within mechanical domain),
⇒ not a tandem transducer
followed by 2. displacement to capacitance
(to the electrical domain)
![Page 7: Slides electrical instrumentation lecture 2](https://reader031.fdocuments.in/reader031/viewer/2022020105/556491c7d8b42a5f6c8b4e93/html5/thumbnails/7.jpg)
7
ET8.017El. Instr.Delft University of Technology
Transduction to the electrical domain:
One sensitivity plus up to 5 cross-sensitivities
Transduction
ma,ma me,ma th,ma opt,ma ch,ma el,ma
ma,me me,me th,me opt,me ch,me el,me
ma,th me,th th,th opt,th ch,th el,th
ma,opt me,opt th,opt opt,opt ch,opt el,opt
ma,ch me,ch
Ma t t t t t tMe t t t t t tTh t t t t t t = Opt t t t t t t
ElCh t
⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠ ma,el me,el th,el opt,el ch,el el,el
os
os
os
os
th,ch opt,ch ch,ch el,ch
s
o
o
s
MaMeTh +Op
MaMeThOptChElt t t
tt t t t t Ch
t t t El
⎛ ⎞ ⎛ ⎞⎛ ⎞⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟
⎝ ⎠ ⎝ ⎠⎝ ⎠
Example: A photodiodeSensitivity: topt,el
Cross-sensitivities: tel,el (?) tth,el (?)Offset: due to dark current
ET8.017El. Instr.Delft University of Technology
• Self generating sensors• Modulating sensors
Transduction to the electrical domain:
Transduction
ma,ma me,ma th,ma opt,ma ch,ma el,ma
ma,me me,me th,me opt,me ch,me el,me
ma,th me,th th,th opt,th ch,th el,th
ma,opt me,opt th,opt opt,opt ch,opt el,opt
ma,ch me,ch
Ma t t t t t tMe t t t t t tTh t t t t t t = Opt t t t t t t
ElCh t
⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠ ma,el me,el th,el opt,el ch,el el,el
os
os
os
os
th,ch opt,ch ch,ch el,ch
s
o
o
s
MaMeTh +Op
MaMeThOptChElt t t
tt t t t t Ch
t t t El
⎛ ⎞ ⎛ ⎞⎛ ⎞⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟
⎝ ⎠ ⎝ ⎠⎝ ⎠
Two types of sensors:
![Page 8: Slides electrical instrumentation lecture 2](https://reader031.fdocuments.in/reader031/viewer/2022020105/556491c7d8b42a5f6c8b4e93/html5/thumbnails/8.jpg)
8
ET8.017El. Instr.Delft University of Technology
+ No additional sources of uncertainty+ No external power supply- Draws all its energy from the measurand
(mechanical source loading)
Self-generating sensors: Example: Potentiometer
Transduction
ET8.017El. Instr.Delft University of Technology
- Optical domain ⇒ additional sourcesof uncertainty (e.g. light intensity)
+ Takes less energy from the measurand(non-contact displacement measurement)
Modulating sensors:Example: Optical encoder
Transduction
![Page 9: Slides electrical instrumentation lecture 2](https://reader031.fdocuments.in/reader031/viewer/2022020105/556491c7d8b42a5f6c8b4e93/html5/thumbnails/9.jpg)
9
ET8.017El. Instr.Delft University of Technology
Resistive sensors
Force sensors using strain gaugesResistance value is defined by specific resistivity and dimensions:
ρρ
∂ ∂ ∂ ∂R L A= + -R L A
ρ LR =A
In case of strain (deformation) due to mechanical stress:
When assuming constant volume:
V L A0V L A∂ ∂ ∂
= → = −
ET8.017El. Instr.Delft University of Technology
Resistive sensors
Force sensors using strain gaugesResistance value is defined by specific resistivity and dimensions:
ρρ
∂ ∂ ∂ ∂R L A= + -R L A
ρ LR =A
In case of strain (deformation) due to mechanical stress:
When assuming constant volume:
k= gauge factor
TENSILE STRESS in sensitive direction:
strain
R 0RΔ⎛ ⎞ >⎜ ⎟
⎝ ⎠
ρρ
:
V L A0R L LV L A 2L R L LMetal film
k
L
∂ ∂ ∂ ⎫= → = − ⎪ ∂ ∂ ∂⎪ → = =⎬∂ ∂ ⎪∝⎪⎭
![Page 10: Slides electrical instrumentation lecture 2](https://reader031.fdocuments.in/reader031/viewer/2022020105/556491c7d8b42a5f6c8b4e93/html5/thumbnails/10.jpg)
10
ET8.017El. Instr.Delft University of Technology
Force sensors using strain gaugesResistance value is defined by specific resistivity and dimensions:
ρρ
∂ ∂ ∂ ∂R L A= + -R L A
ρρ
:
V L A0R L LV L A 2
L R L Lk
Metal filmL
∂ ∂ ∂ ⎫= → = − ⎪ ∂ ∂ ∂⎪ → = =⎬∂ ∂ ⎪⎪⎭
ρ LR =A
In case of strain (deformation) due to mechanical stress:
When assuming constant volume:
k= gauge factor
comp tens
R RR RΔ Δ⎛ ⎞ ⎛ ⎞= −⎜ ⎟ ⎜ ⎟
⎝ ⎠ ⎝ ⎠
COMPRESSIVESTRESS in sensitive direction:
Resistive sensors
ET8.017El. Instr.Delft University of Technology
Force sensors using strain gaugesResistance value is defined by specific resistivity and dimensions:
ρρ
∂ ∂ ∂ ∂R L A= + -R L A
ρ LR =A
In case of strain (deformation) due to mechanical stress:
When assuming constant volume:
k= gauge factor
Applying load in insensitive direction:
Δ
.perp
R 0R
⎛ ⎞ ≈⎜ ⎟⎝ ⎠
Resistive sensors
ρρ
:
V L A0R L LV L A 2
L R L Lk
Metal filmL
∂ ∂ ∂ ⎫= → = − ⎪ ∂ ∂ ∂⎪ → = =⎬∂ ∂ ⎪⎪⎭
![Page 11: Slides electrical instrumentation lecture 2](https://reader031.fdocuments.in/reader031/viewer/2022020105/556491c7d8b42a5f6c8b4e93/html5/thumbnails/11.jpg)
11
ET8.017El. Instr.Delft University of Technology
Measuring force in two dimensions
Resistive sensors
ET8.017El. Instr.Delft University of Technology
Wheatstone bridge:
Information is contained in the differential signal:
( ) ( )1 2b bR R R RU = U U
R R R R R+ Δ + Δ
=+ Δ + − Δ
1 2 10 10b bdR= mV at U VU U U UR
Δ< == −
( ) ( )2 2b bR R R RU = U U
R R R R R− Δ − Δ
=+ Δ + − Δ
Which, however, is superimposed on the common-mode signal:
1 2 5 102 2
bc b
U U UU V at U V+= = = =
The Wheatstone bridge
![Page 12: Slides electrical instrumentation lecture 2](https://reader031.fdocuments.in/reader031/viewer/2022020105/556491c7d8b42a5f6c8b4e93/html5/thumbnails/12.jpg)
12
ET8.017El. Instr.Delft University of Technology
Bridge configurations
• Linear• All elements onstructure
• Increasing ANDdecreasing withmeasurand
Full bridge
1/2 bridge• Non-linear• ½ of elements onstructure
• Increasing ORdecreasing withmeasurand
1/4 bridge• Non-linear• 1/4 of elements onstructure-minimumdimensions.
ET8.017El. Instr.Delft University of Technology
Very suitable for displacement measurements
Capacitive sensor readout
ε ε ε= =o r oA ACh h
Lateral
From the parallel-plate approximation:
( )Δε
−= o
ow x x
Ch
εΔ
ε
=+
=
o
o o
ACh zACh
εΔ
εΔ
=+
=−
u o
l o
ACh z
ACh z
( )
εΔ Δ
εΔΔ ε ΔΔ
⎛ ⎞− = − =⎜ ⎟− +⎝ ⎠⎛ ⎞⎜ ⎟= ≈⎜ ⎟+⎝ ⎠
/ /
//
l u o
oo 2 2
A 1 1C Ch 1 z h 1 z h
2 AA 2 z hC zh h1 z h
Vertical Vert. differentially
Non-linearity reduced by differential measurement
o o1 1C C C Ah h z
Δ εΔ
⎛ ⎞= − = − =⎜ ⎟+⎝ ⎠
Non-linear/
o o2 2
z1 z
A A zh h hε ε ΔΔ
Δ+≈
Linear
![Page 13: Slides electrical instrumentation lecture 2](https://reader031.fdocuments.in/reader031/viewer/2022020105/556491c7d8b42a5f6c8b4e93/html5/thumbnails/13.jpg)
13
ET8.017El. Instr.Delft University of Technology
MEMS Microphone
Sound waves move membrane ⇒ capacitance between the membrane and the fixed back plate variesFound in many cell phones
Courtesy: R. van Veldhoven, NXPCourtesy: Akustica (website)
ET8.017El. Instr.Delft University of Technology
The charge amplifier (1)
For an “ideal” opamp:
(a) U-= U+= 0(b) Is(ω)= jωCs. Ui(ω)(c2) It(ω) = -jωCt. Uo(ω), hence:
Uo(ω)/ Ui(ω) = -Cs/Ct
(can also be derived from the expression of an inverting amplifier with: Zs=1/ jωCs and Zt= 1/ jωCt)
Capacitive sensor readout
Use Cs for lateral displacement sensing (Uo∝A) and Ct for vertical displacement sensing with linear output (Uo∝ 1/(1/d)=d) .
ε ε ε= =o r oA ACh h
![Page 14: Slides electrical instrumentation lecture 2](https://reader031.fdocuments.in/reader031/viewer/2022020105/556491c7d8b42a5f6c8b4e93/html5/thumbnails/14.jpg)
14
ET8.017El. Instr.Delft University of Technology
The charge amplifier (2)
In practice:1. Rt required to avoid saturation
of the output by Ibias.
2. Open-loop gain is finite: A(ω) = Ao/(1+jωτv).
For an “ideal” opamp:
Uo(ω)/ Ui(ω) = -Cs/Ct
Capacitive sensor readout
ET8.017El. Instr.Delft University of Technology
Modulus transfer of the charge amplifier
2. U- is virtual ground and can be used for adding currents in a differential sensor structure.
For sensor readout the charge amplifier typically attenuates the excitation voltage Ui (Cs«Ct).
Features:1. Can be used for excitation voltage frequencies up to ωT.
( )1 1
to s
i vt t
o
-jU CR=U + j + j R C
A
ωτω ω⎛ ⎞
⎜ ⎟⎝ ⎠
Capacitive sensor readout
![Page 15: Slides electrical instrumentation lecture 2](https://reader031.fdocuments.in/reader031/viewer/2022020105/556491c7d8b42a5f6c8b4e93/html5/thumbnails/15.jpg)
15
ET8.017El. Instr.Delft University of Technology
Application in differential sensor readout
Capacitive sensor readout
Topology is often used for the readout of MEMS accelerometers and gyroscopes
ET8.017El. Instr.Delft University of Technology
Piezo-electricityPiezo-electric force sensors
Not deformed: no polarization charge
Shear piezo-electric sensitivity (Normal) piezo-
electric sensitivityPiezo-electricity is reversible: connecting voltage source results ina deformation and, hence, in force.
Piezo-electricity in all crystal directions: described by a matrix.
![Page 16: Slides electrical instrumentation lecture 2](https://reader031.fdocuments.in/reader031/viewer/2022020105/556491c7d8b42a5f6c8b4e93/html5/thumbnails/16.jpg)
16
ET8.017El. Instr.Delft University of Technology
Application in acceleration sensing
Charge sensitivity: Sq= 5 pC/N.Capacitance: Cs= 20 pFMass: M= 100 g.
Uoa @ 1 m/s2 ?
Piezo-electric force sensors
Force due to load: F= M.a= 0.1 NVoltage sensitivity: Su= Sq/Cs= 250 mV/N.Hence: Uo= 25 mV
ET8.017El. Instr.Delft University of Technology
Magnetic field sensor using the Hall Effect
The Hall effect is based on the Lorentz force acting on electrons moving through a (semi)conductor.
The deflection results in charge accumulation. The electrostatic field due to the charge counteracts the Lorentz force and equilibrium is reached at the Hall field, EH= FL/e= vB.The Hall voltage UH= EH.w is the output signal and is proportional to both I and B.
Note that UH/I=f(B) is like a resistance measured in a 4-terminal resistance measurement.
![Page 17: Slides electrical instrumentation lecture 2](https://reader031.fdocuments.in/reader031/viewer/2022020105/556491c7d8b42a5f6c8b4e93/html5/thumbnails/17.jpg)
17
ET8.017El. Instr.Delft University of Technology
Magnetic field sensor using the Hall Effect
Stress in the conductive layer results in offset.
Wheatstone bridge not balanced at B= 0 T.
ET8.017El. Instr.Delft University of Technology
Changing the direction of the bias current changes the relative polarity of Voff & Vhall
So averaging the bridge output cancels Voff !
In practicen-well resistance depends on current direction (anisotropic)
⇒ 3 current directions needed for optimal offset cancellation!
The spinning current technique
![Page 18: Slides electrical instrumentation lecture 2](https://reader031.fdocuments.in/reader031/viewer/2022020105/556491c7d8b42a5f6c8b4e93/html5/thumbnails/18.jpg)
18
ET8.017El. Instr.Delft University of Technology
Spinning-Current Hall Plate
3 current directions ⇒ Octagonal Hall plateBias current rotated, while Hall voltages are summedCancels offset due to static bridge mismatch
⇒ 10 - 100µT offset
Earth’s magnetic field ~ 50µT
So electronic compass applications are possible …
ET8.017El. Instr.Delft University of Technology
Smart Hall Sensor
Standard 0.5μm CMOSSpinning current technique + low-offset amplifier⇒ 4µT offsetState-of-the-art!
J. van der Meeret al., ISSCC ‘05
Hall Sensor Inst. Amp. ADC
Timing, Control & Interfaces
![Page 19: Slides electrical instrumentation lecture 2](https://reader031.fdocuments.in/reader031/viewer/2022020105/556491c7d8b42a5f6c8b4e93/html5/thumbnails/19.jpg)
19
ET8.017El. Instr.Delft University of Technology
The Seebeck effect is due to the excess kinetic energy of free carriers at the hot side of a (semi)-conducting material, which results in a net diffusion of carriers towards the cold side. The resulting charge build-up creates an internal electric field that opposes further diffusion and is externally measurable as an open-circuit potential, ΔV (conventional).
Equivalent definition: The Seebeck effect is due to the temperature–dependence of the Fermi level in a material (quantum mechanical).
F
T
E1q T∂
=∂
α
,T
VT∂
=∂
α where α is the temperature coef of the Seebeck voltage at temperature T⇒ the Seebeck coefficient
The Seebeck effectTemperature sensors
ET8.017El. Instr.Delft University of Technology
Practical use of the Seebeck effect:a thermocouple with two different materialsand a temperature difference
( ) ( ) ( )α α α α
α α α, , , ,. . . .a T1 1 b T1 1 b T 2 2 a T 2 2
a b 1 2 ab 1 2
T - T T - T
- T -T T -T
⎡ ⎤ ⎡ ⎤= +⎣ ⎦ ⎣ ⎦=
MATERIALCOMB. SENSITIVITY (AT 0°C) [μV/K]
RANGE [°C)]
iron/constantan 45 0..760 copper/constantan 35 -100..370 chromel/alumel 40 0..1260 platinum/Pt+ Rd 5 0..1500
Temperature sensors
No offset, however very small DC voltages (typ.< 1mV) are generated.
![Page 20: Slides electrical instrumentation lecture 2](https://reader031.fdocuments.in/reader031/viewer/2022020105/556491c7d8b42a5f6c8b4e93/html5/thumbnails/20.jpg)
20
ET8.017El. Instr.Delft University of Technology
Thermopile for increased output signal
Problem: readout circuit has offset
Temperature sensors
Problems:- increased electrical resistance(noise)
- increased thermal conductionbetween cold and hot parts ⇒1. Increased source loading or2. More heat flux required to build
up a temperature difference.
N-times the thermocouple voltage
ET8.017El. Instr.Delft University of Technology
A Smart Wind Sensor!
Convective cooling ⇒ temperature gradient⇒ wind speed and direction
![Page 21: Slides electrical instrumentation lecture 2](https://reader031.fdocuments.in/reader031/viewer/2022020105/556491c7d8b42a5f6c8b4e93/html5/thumbnails/21.jpg)
21
ET8.017El. Instr.Delft University of Technology
Thermal Wind Sensor
On-chip thermopiles measure temperature gradientK. Makinwa et al., ISSCC ‘02
ET8.017El. Instr.Delft University of Technology
Smart Temperature Sensors
Transistors are natural temperature sensorsBut manufacturing tolerances causeerrors of up to 3°C
?
![Page 22: Slides electrical instrumentation lecture 2](https://reader031.fdocuments.in/reader031/viewer/2022020105/556491c7d8b42a5f6c8b4e93/html5/thumbnails/22.jpg)
22
ET8.017El. Instr.Delft University of Technology
BJT Characteristics: VBE
VBE is a near-linear function of temperatureWith a negative temperature coefficient: ~ –2mV/°CBut it is process dependent (via IS and IC)
collector
emitter
base
+VBE–
IC
• For IC >> IS
exp
ln
BEC S
CBE
S
qVI IkT
IkTVq I
⎛ ⎞≈ ⎜ ⎟⎝ ⎠
⇒ =
ET8.017El. Instr.Delft University of Technology
BJT Characteristics: ΔVBE
By biasing two transistors at a fixed collector current ratio p, we can eliminate the process dependence:
ΔVBE is a linear function of temperature
With a positive tempco: ~ 180µV/°C (for p·r =10)
collector
emitterr·AE
base
+VBE1–
I collector
emitterAE
base
+VBE2–
p·I
)ln(12 rpq
kTVVV BEBEBE ⋅=−=Δ
![Page 23: Slides electrical instrumentation lecture 2](https://reader031.fdocuments.in/reader031/viewer/2022020105/556491c7d8b42a5f6c8b4e93/html5/thumbnails/23.jpg)
23
ET8.017El. Instr.Delft University of Technology
Operating Principles (1)
Two bipolar transistors can generate:ΔVBE proportional to absolute temperature (PTAT)VBE complementary to absolute temperature (CTAT)
ET8.017El. Instr.Delft University of Technology
Operating Principles (2)
These voltages can be combined to give:VREF temperature independent (band-gap) voltageα·ΔVBE temperature dependent voltage
Their ratio is a measure of temp:BEBE
BE
VVVΔ⋅α+
Δ⋅α=μ
![Page 24: Slides electrical instrumentation lecture 2](https://reader031.fdocuments.in/reader031/viewer/2022020105/556491c7d8b42a5f6c8b4e93/html5/thumbnails/24.jpg)
24
ET8.017El. Instr.Delft University of Technology
Current mirror ratio p, emitter arearatio r and amplifier gain α generate
Current source Ibias generates VBE
ADC then computes the ratio:
( )rpq
kTVPTAT ⋅α= ln
REF
PTAT
BEBE
BE
VV
VVV
=Δ⋅α+
Δ⋅α=μ
A practical Bandgap temperature sensor
ET8.017El. Instr.Delft University of Technology
• CMOS ⇒ substrate PNPs
• IS spread? ⇒ one room temperature trim• Inaccuracy < ±0.1°C (3σ) from –55 to125°C
Pertijs et al., JSSC, Dec. ‘05
State-of-the-Art
![Page 25: Slides electrical instrumentation lecture 2](https://reader031.fdocuments.in/reader031/viewer/2022020105/556491c7d8b42a5f6c8b4e93/html5/thumbnails/25.jpg)
25
ET8.017El. Instr.Delft University of Technology
Assignment 2a
The accuracy of a bandgap temp sensor will be limited by the offset and gain error of the “α” amplifierAssuming p=1, r=16 and α = 8, what offset corresponds to 0.1°C error? Similarly what gain error corresponds to an error of less than 0.1°C over the military range -55°C to 125°C?Assume that the tempco of VBE = -2mV/°C and that ideally, VREF = 1.2V Please submit this before the class on Wed. 19 Sept.
BEBE
BE
VVVΔ⋅α+
Δ⋅α=μ
ET8.017El. Instr.Delft University of Technology
Assignment 2b
Derive an expression for the transfer function IL/Ii of the circuit shown above.Assuming the opamp suffers from offset and bias current, calculate the corresponding detection limit Please submit this before the class on Wed. 19 Sept.
![Page 26: Slides electrical instrumentation lecture 2](https://reader031.fdocuments.in/reader031/viewer/2022020105/556491c7d8b42a5f6c8b4e93/html5/thumbnails/26.jpg)
26
ET8.017El. Instr.Delft University of Technology